93 



excentric anomaly being found, the true anomaly is had by a well 

 known theorem. 



This folution of Kepler's is perhaps, in praftical value, little inferior 

 to any that has been fince given ; it obvioufly requires only two im- 

 provements, a near approximation to begin the computation, and alfo 

 at once from the error of the computed mean anomaly, to derive the 

 correftion of the firll afTumed excentric anomaly. The fecond CafTuii* has 

 given a rule for the former, and applying this rule of Caffini's to a me- 

 thod given by Sir Ifaac Newton,! a correftion is at once obtained, which 

 will give the excentric anomaly, true to lefs tlian a fecond in all the 

 planets, as is hereafter fliewn. 



On BouUiald^ firjl Hypothefis and its fimpUficaiion by Sctb Ward, com- 

 monly known by the name of the fimple elliptic Hypothefis. 



Kepler's difcoveries refled fimply on obfervations, and on obfervations, 

 which, from the neceffary imperfeftion of inflruments, were liable to 

 errors within certain limits. Any other hypothefes which would agree 

 with obfervations within thefe hmits, were confidered as equally en- 

 titled to notice, as the laws of Kepler. Accordingly, Ifmael Boulliald, 

 one of the greatefl mathematicians of his time, adopted only the ellip- 

 tic orbit, and not the equable defcription of areas. Defirous of deriv- 

 ing the inequable motion in the orbit, from an equable motion, he fup- 

 pofed " the ellipfe, in which the planet moved to be a feftion of a 

 *' certain cone, the axis of which paffed through the higher focus, and 

 " in which ellipfe, the motion was fo regulated by fome phyfical caufe, 



" that 



* Mem. Acad. 1719, f Math, Prin. Nat. Phil. Lib. i. Seft, 6. Schol. 



